Answer:
<em>a) x = -2+√3 and -2-√3</em>
<em>b) x = -1 + 2√3/3 and -1 - 2√3/3</em>
<em>c) x = 3.185 and 0.315</em>
Step-by-step explanation:
To solve the following quadratic equation, we will use the general formula
x = -b±√b²-4ac/2a
a) x²+4x+1 = 0
a = 1, b = 4 and c = 1
Substitute into the formula
x = -4±√4²-4(1)(1)/2(1)
x = -4±√16-4/2
x = -4±√12/2
x = -4±2√3/2
x = (-4+2√3)/2 and (-4-2√3)/2
<em>x = -2+√3 and -2-√3</em>
b) 3x²+6x-1 = 0
a = 3, b = 6 and c = -1
Substitute into the formula
x = -6±√6²-4(3)(-1)/2(3)
x = -6±√36+12/6
x = -6±√48/6
x = -6±4√3/6
x = (-6+4√3)/6 and (-6-4√3)/6
<em>x = -1 + 2√3/3 and -1 - 2√3/3</em>
<em></em>
c) 2x² - 7x + 2 = 0
a = 2, b = -7 and c = 2
x = -(-7)±√(-7)²-4(2)(2)/2(2)
x = 7±√49-16/4
x =7±√33/4
x = 7±5.74/4
x = 7+5.74/4 and 7-5.74/4
x = 12.74/4 and 1.26/4
<em>x = 3.185 and 0.315</em>
<em></em>
Answer:
He is 5.6 km away
Step-by-step explanation:
he starts traveling away from base and is 8.3 km away to start with
then he turns west and travels 13.9 km away
what this mean is that you have to subtract the distance he turned from the distance he started off with
ex: 13.9 - 8.3 = 5.9
to get your answer of how far away he is from the base
Marcus went above his budget as 25% percent of his allowance would be $5, and he went $2.42 over.
Answer:
y= -4/3x - 1/2 is the perpendicular line to y= 3/4x -1/2
Step-by-step explanation:
The slope would be the negative reciprocal of your current slope :)
+3/4 would turn into -4/3 and you wouldnt change the y intercept
hope this helps
Use the point-slope form of the equation of a line:-
y - y1 = m(x - x1)
y - 4 = 4(x - 2)
y - 4 = 4x - 8
4x - y = 4 is the answer
